I still don’t understand how mathematicians use math in the real world and how they figure this out
In: Mathematics
Math was invented, first, as an applied tool. We derived math *from* the real world, so that’s how we know we can link it to it.
Later, as Math became its own thing, we began to think about it more abstractly, as a subject of inquiry unto itself, and there stopped being a guarantee that it would link to anything in the real world.
In the end, today, Math has a variety of disciplines and subjects. “Math” isn’t a whole, cohesive thing, but rather has many branches. Some of them tie very strongly to the real world because they are designed to do so; we observe the real world and derive the mathematical equations that describe it. Others are more abstract; we come up with some set of rules and see what mathematical conclusions we can draw from those rules, without regard to whether there are any real-world applications.
It’s the other way around. People didn’t have math that they tried to apply to the real world but had real world problems that they tried to solve with numbers.
Things like how many coins do I owe you? How many cows do I have? How much wheat do I need to survive the winter?
As the world became more and more complex, so did the problems that needed to be solved by math. For a very long time these real world problems drove the development of more complex mathematics.
How fast will this train go? How much fuel will this plane need? What’s the likely outcome of this event? What’s the distance between these two planets? What will the weather be like tomorrow? What will happen if these two particles collide? What’s the optimal path between multiple routes?
We just recently reached a point that we have more “math” that we can use right now, and scientists later realize that they can use an already existing “math” to solve a real world problem.
* Math is just another language used to describe the real world.
* It’s not that there was math and separately the real world and someone discovered that math could work with it, but rather over time people developed a way to describe amounts of things in the world.
* If anything, the discovery was that math that was developed to describe the way one real world thing works, also was found to describe how a totally different real world thing works.
* But what the really means is that there are fundamental concepts that govern how the whole real-world works, and math can be used to describe them too.
As the other replies have indicated, math is invented in order to help solve real world problems. Arithmetic is about numbers, and the higher branches of math are about things that are NOT numbers (what it means to add, subtract, etc., shapes, sets of objects, vectors, functions, etc.).
So mathematicians typically focus on “theoretical” math – inventing new branches of math, and/or resolving various theorems within math that haven’t been proven yet.
While the term [applied mathematics](https://en.wikipedia.org/wiki/Applied_mathematics) (as opposed to “theoretical mathematics”) exists, it’s still about creating new models or branches of math to resolve specific problems.
So basically, the people who “use math in the real world” are mostly NOT mathematicians per se – they’re physicists, biologists, etc., other sciences use math a lot. Math is the underlying tool.
It’s similar to how “the people who use languages in the real world” are not necessarily linguists. Language is the tool that’s used by everyone to communicate.
Math works by having assumptions and seeing what implications they have.
We make lots of assumptions about the world around us. These assumptions can be studied in math framework. You can see what implications they have, and then check out reality if those predictions of math end up being part of reality. If yes, well, you are probably interested in seeing if you could replicate this feat of prediction.
Math is not really restricted in any way to the reality though. Assumptions you make in math land don’t have to have anything to do with reality. Plenty of areas of math are based on assumptions that were thought to be outlandishly silly and inconceivable to be part of reality. Until 10 or 100 or 1000 years later we found out that some aspect of reality actually fits all those assumptions and we can use that math to predict that thing.
Math works in the real world through the use of units. 1 = 1 in math. 1 carrot = 1 carrot works in the real world based on how you define a carrot. Carrots vary greatly in size so the equation works if you accept the units but may produce unexpected results – you could be saying a tiny carrot is equal to a large carrot.
With engineering, physics, chemistry, etc the key thing that makes them work is units. F=ma is not generically true. The units have to be correct. If you use F and m in metric units but acceleration in furlongs per fortnight your answer will be wrong.
Math was made to understand the otherwise chaotic real world, how else would you know the yield point of a steel column for example? maths can be applied to everything to make things easier and safer.
You have eight sheep. I want five sheep for three silver pieces per sheep. How much silver do I need to pay you and how many sheep will you have after that?
The first mathematics we ever did was pretty much just that: basic counting or doing basic business transactions. It took a good number of millennia before math *could* be done without linking it directly to the real world.
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